The fifty-eighth hexagram, Dui ("The Joyous" or Lake), is one of the eight doubled hexagrams, formed of the trigram Dui (Lake) above and below. Two lakes joined, feeding and replenishing one another, give the image of open, shared gladness. It stands fifty-eighth in the King Wen sequence.
Dui stands tenth of 64 in the xiantian, or Earlier Heaven, arrangement, the binary ordering devised by Shao Yong in the eleventh century and ascribed to Fu Xi, distinct from its fifty-eighth place in the King Wen sequence traced above, and again distinct from the trigram Dui's own place in the eight-trigram form of the same circle. This was the arrangement Joachim Bouvet, a Jesuit in Beijing, sent to Gottfried Wilhelm Leibniz in 1701, letting Leibniz read its broken and unbroken lines as his own binary 0 and 1.
Read from the bottom, the six lines of The Joyous run yang, yang, yin, yang, yang, yin. A later interpretive layer absent from the original Zhou Yi, the nuclear hexagram (hu gua), treats lines two through four as a lower trigram and lines three through five as an upper one; here they combine as Xun over Li, forming hexagram 37, The Family (Jia Ren), a hidden figure first associated with the Han-dynasty scholar Jing Fang, whose Yijing commentary of the first century BCE is credited with the earliest appearance of nuclear trigrams. The Joyous's King Wen partner is hexagram 57, The Gentle (Xun); most of the sixty-four pair this way, related by turning the whole figure upside down, while the eight hexagrams built from a single doubled trigram pair instead by inverting every line. Mawangdui (1973) orders hexagrams by trigram, not King Wen; names here follow Wilhelm and Baynes, 1950, not Legge, 1882.